If you are accessing the DLC from the Steam in-game web browser, you won't be able to download the DLC from the Download Your Purchase Now button in Step 5. Please follow these additional steps to download the aircraft.

6. Restart Microsoft Flight.
7. Go to the Hangar.
8. The RED TAILS P-51 aircraft should now show in your list of aircraft. (It may take a moment or two after signing in.)
9. Select the RED TAILS P-51 and click Redownload.
10. Click Confirm Download from the Games for Windows--LIVE guide.

The RED TAILS P-51 should now start downloading and appear in your hangar for use after it is done.

Didn't work for me. Here's what happened after I typed my name/password:http://screencast.com/t/V0w82qNWf
Now that comes up any time I hit "Buy for PC."
EDIT: Solved it by using IE instead of Chrome. Only Microsoft...